Mathematics · Real Analysis

Let E be a bounded subset of &double;R. If α = glb(E) is the greatest lower bound of E, then for each ε > 0, there exists x ∈ E such that:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1x ≤ α - ε
2x ≥ α + ε
3α - ε < x ≤ α
4α ≤ x < α + ε✓

Correct answer

α ≤ x < α + ε

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Let E be a bounded subset of &double;R. If α = glb(E) is the greatest lower bound of E, then for each ε > 0, there exists x ∈ E such that:

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Let E be a bounded subset of &double;R. If α = glb(E) is the greatest lower bound of E, then for each ε > 0, there exists x ∈ E such that:

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